aka Multivibrator.
Very simple operation -
One base switches its transistor on first, due to tolerance imbalances between components. (eg Q1).
That capacitor, C1 discharges through Q1 c-e junction, completing ground-path for C1.
Due to discharge, other plate of C1, connected to Q2b, gets pulled negative, switching Q2 off.
This allows C2 to charge up as no path to ground.
Meanwhile, already discharged C1 no longer negative so R2 feeds a positive bias to Q2 base until Q2 conducts, discharging C2 and switching Q1b off. So the cycle continues....
Note: Waveform on collectors is not true square due to charging capacitors.
The RC values set the time constant for each half, so adjustment of mark-space ratio is possible.
For a truer square wave, emitter-base couple a third transistor to the multivibrator.
Q3b must go to Q1e or Q2e. Then load on Q3c.